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Ancilla-Based Fortification of Phase Super-Sensitivity in Two-Photon Interferometery

Walker D. Larson, Bahaa E. A. Saleh

Published Nov 4, 2016• 0 citations
OpenAlex

Abstract

The super-sensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots -- phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point of the sensor to a less vulnerable phase value. We present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an adaptive estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally super-sensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.

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The super-sensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots -- phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point of the sensor to a less vulnerable phase value. We present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an adaptive estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally super-sensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.
The supersensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots---phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point to a less vulnerable phase value. Since this is not always feasible, we present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally supersensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.
Recent advances in quantum photonics have enabled increasingly robust protocols in optical phase estimation, achieving precisions beyond the standard quantum limit and approaching the Heisenberg limit. While intrinsic losses hinder the realization of unconditional super-sensitivity, reaching quantum advantage, defined as sensitivity surpassing that of any classical counterpart with identical resources, remains achievable. Here we experimentally demonstrate such an advantage using a fully fibered Mach-Zehnder-type interferometer operating at telecom wavelengths, free of post-selection. The scheme relies on the conversion of polarization-entangled photon pairs, a degree of freedom commonly favored for experimental convenience, into energy-time entanglement, which is particularly well suited for scalable fiber-based sensors. All system imperfections, including asymmetric losses and detector inefficiencies, are accounted for in the Fisher information analysis, yielding a measured quantum advantage of 10%. This result highlights the practicality of compact, alignment-free quantum interferometers for real-world sensing applications.
It is well-known that the super-sensitivity of phase estimation in two-photon interferometery is diminished by the effect of decoherence. Specific to the paradigm of local phase estimation, any presence of decoherence removes all sensitivity to small shifts in the neighborhood of certain phases. For estimates of the phase difference between two arms of an interferometer using two-photon coincidence measurements, all sensitivity is lost for phase differences in the neighborhood of π/2. The benefit of employing an ancillary optical degree of freedom alongside the principal interfering degree of freedom was recently found to fortify super-sensing two-photon states against the debilitating effect of spectral distinguishability: an effect that reduces the visibility of two-photon interference. In the present work, we investigate the use of an ancillary degree of freedom when measuring a phase shift by use of a two-photon Mach-Zehnder-interferometer contaminated by a depolarizing channel causing decoherence: an effect that reduces both two-photon and single-photon interference visibility. We model our input state as single photons entering both input ports of an interferometer. The principal interferometer-path modes are coupled to polarization, and decoherence is modeled by replacing the density matrix describing this input with a maximally mixed state with some probability p. We calculate the sensitivity through the quantum fisher information, finding that the process of fortifying input states retains sensing at or above the standard quantum limit in the neighborhood of phase differences around π/2, for all probabilities below 1/4 — an advantage impossible without employing the ancillary degree of freedom.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
We propose a phase estimation protocol for optical interferometry that employs a probe state (containing on average n‾\overline{n}n photons) obtained by squeezing each mode, separately, of a single photon path entangled Bell state. This scheme involves a Mach-Zehnder type interferometer for which each mode is squeezed after the first beam splitter. Information about the differential phase is extracted using a parity detection and the resulting measurement signal is super-resolving and supersensitive, with a minimum phase uncertainty $\ensuremath{\Delta}\ensuremath{\varphi}=2/(\overline{n}+1)$. This probe state can be generated with current technologies where n‾\overline{n}n is in the order of many thousands of photons.
With the rapid development of quantum technologies in recent years, the need for high-sensitivity measuring techniques has become a key issue. In particular, optical sensors based on quantum states of light have proven to be optimal resources for high-precision interferometry. Nevertheless, their performance may be severely affected by the presence of noise or imperfections. In this work, we derive the quantum Fisher information matrix associated with the simultaneous estimation of an interferometric phase and the indistinguishability characterizing the probe state consisting of an even number of photons. We find the optimal measurement attaining the ultimate precision for both parameters in a single setup and perform an experiment based on a pair of photons with an unknown degree of indistinguishability entering a two-port interferometer.